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Graph-Rewriting Automata (GRA) are an extension of Cellular Automata to a dynamic structure using local graph-rewriting rules. This work introduces linear algebra based tools that allow for a practical investigation of their behavior in…
In this dissertation, we study two of the global properties of 1-dimensional cellular automata (CAs) under periodic boundary condition, namely, reversibility and randomness. To address reversibility of finite CAs, we develop a mathematical…
This paper describes a new concept of cellular automaton (CA). XCA consists of a set of arcs (edges) that correspond to cells in CA. At a particular time, the arcs are connected to a directed graph. With each time step, the arcs exchange…
The fields of Origin of Life and Artificial Life both question what life is and how it emerges from a distinct set of "pre-life" dynamics. One common feature of most substrates where life emerges is a marked shift in dynamics when…
Cellular automata (CA) are a class of computational models that exhibit rich dynamics emerging from the local interaction of cells arranged in a regular lattice. In this work we focus on a generalised version of typical CA, called graph…
Anomaly detection suffers from unbalanced data since anomalies are quite rare. Synthetically generated anomalies are a solution to such ill or not fully defined data. However, synthesis requires an expressive representation to guarantee the…
Recent theories suggest that Neural Scaling Laws arise whenever the task is linearly decomposed into power-law distributed units. Alternatively, scaling laws also emerge when data exhibit a hierarchically compositional structure, as is…
We have designed a machine that becomes increasingly better at behaving in underspecified circumstances, in a goal-directed way, on the job, by modeling itself and its environment as experience accumulates. Based on principles of…
This study presents a theoretical model for a self-replicating mechanical system inspired by biological processes within living cells and supported by computer simulations. The model decomposes self-replication into core components, each of…
The year of 2024 marks the 25th anniversary of the publication of evoloops, an evolutionary variant of Chris Langton's self-reproducing loops which proved constructively that Darwinian evolution of self-reproducing organisms by variation…
We propose a characteristic representation ofone-dimensional and 2-state, 3-neighbor cellular automaton rules, which describes an effective form of each rule after many time steps. Simulated results of the representation show that complex…
The local structure theory for cellular automata (CA) can be viewed as an finite-dimensional approximation of infinitely-dimensional system. While it is well known that this approximation works surprisingly well for some cellular automata,…
Neural Cellular Automata (NCA) have shown a remarkable ability to learn the required rules to "grow" images, classify morphologies, segment images, as well as to do general computation such as path-finding. We believe the inductive prior…
We investigate number conserving cellular automata with up to five inputs and two states with the goal of comparing their dynamics with diffusion. For this purpose, we introduce the concept of decompression ratio describing expansion of…
A general framework for the simulation of reaction-diffusion systems with probabilistic cellular automata is presented. The basic reaction probabilities of the chemical model translate directly into the transition rules of the automaton,…
We present a method to eliminate redundancy in the transition tables of Boolean automata: schema redescription with two symbols. One symbol is used to capture redundancy of individual input variables, and another to capture permutability in…
We consider the problem of finding the density of 1's in a configuration obtained by $n$ iterations of a given cellular automaton (CA) rule, starting from disordered initial condition. While this problems is intractable in full generality…
We develop a formal model of the emergence of self-constructing objects (e.g. heteropolymers with autocatalytic capability) in an open system, which don't contain such objects initially. The objects are constructed from subunits (e.g.…
We explain how hierarchical organization of biological systems emerges naturally during evolution, through a transition in the units of individuality. We will show how these transitions are the result of competing selective forces operating…
Commonly studied cellular automata are memoryless and have fixed topology of connections between cells. However by allowing updates of links and short-term memory in cells we may potentially discover novel complex regimes of spatio-temporal…